We investigate a new width parameter, the fusion-width of a graph. It is a natural generalization of the tree-width, yet strong enough that not only graphs of bounded tree-width, but also graphs of bounded clique-width, trivially have bounded fusion-width. In particular, there is no exponential growth between tree-width and fusion-width, as is the case between tree-width and clique-width. The n...

We study the existence of polynomial kernels, for parameterized problems without a kernel on general graphs, when restricted to graphs bounded twin-width. Our main result is that k -Dominating Set twin-width at most 4 would contradict standard complexity-theoretic assumption. The reduction quite involved, especially get upper bound down 4, and can be tweaked work Connected Total (albeit with wo...